武汉市在校大学生数与经济增长的协整分析

近二十年来,我国高等教育规模不断扩大,高校在校生数不断增加,其中武汉市位居全国前列．为了研究高校在校生数对当地经济发展的影响,本文利用武汉市1992—2012年在校大学生人数数据,通过建立合适的模型,来定量探讨武汉市在校大学生数与经济增长的内在关系．结果表明,武汉市经济增长与武汉在校大学生人数模型之间存在着长期均衡关系且互为格兰杰因果关系．     

A new family of time-space harmonic polynomials with respect to Lévy processes

By means of a symbolic method, a new family of time-space harmonic polynomials with respect to Lévy processes is given. The coefficients of these polynomials involve a formal expression of Lévy processes by which many identities are stated. We show that this family includes classical families of polynomials such as Hermite polynomials. Poisson–Charlier polynomials result to be a linear combinations of these new polynomials, when they have the property to be time-space harmonic with respect to the compensated Poisson process. The more general class of Lévy–Sheffer polynomials is recovered as a linear combination of these new polynomials, when they are time-space harmonic with respect to Lévy processes of very general form. We show the role played by cumulants of Lévy processes, so that connections with boolean and free cumulants are also stated.     

A hybrid mean value involving two-term exponential sums and polynomial character sums

Let q ? 3 be a positive integer. For any integers m and n, the two-term exponential sum C(m, n, k; q) is defined by \(C(m,n,k;q) = \sum\limits_{a = 1}^q {e((ma^k + na)/q)} \) , where \(e(y) = e^{2\pi iy} \) . In this paper, we use the properties of Gauss sums and the estimate for Dirichlet character of polynomials to study the mean value problem involving two-term exponential sums and Dirichlet character of polynomials, and give an interesting asymptotic formula for it.     

Relations among Henstock,McShane and Pettis integrals for multifunctions with compact convex values

Fremlin (Ill J Math 38:471–479, 1994) proved that a Banach space valued function is McShane integrable if and only if it is Henstock and Pettis integrable. In this paper we prove that the result remains valid also in case of multifunctions with compact convex values being subsets of an arbitrary Banach space (see Theorem 3.4). Di Piazza and Musia? (Monatsh Math 148:119–126, 2006) proved that if $X$ is a separable Banach space, then each Henstock integrable multifunction which takes as its values convex compact subsets of $X$ is a sum of a McShane integrable multifunction and a Henstock integrable function. Here we show that such a decomposition is true also in case of an arbitrary Banach space (see Theorem 3.3). We prove also that Henstock and McShane integrable multifunctions possess Henstock and McShane (respectively) integrable selections (see Theorem 3.1).     

The analyticity of a generalized Ruelle’s operator

In this work we propose a generalization of the concept of Ruelle’s operator for one dimensional lattices used in thermodynamic formalism and ergodic optimization, which we call generalized Ruelle’s operator. Our operator generalizes both the Ruelle operator proposed in [2] and the Perron Frobenius operator defined in [7]. We suppose the alphabet is given by a compact metric space, and consider a general a-priori measure to define the operator. We also consider the case where the set of symbols that can follow a given symbol of the alphabet depends on such symbol, which is an extension of the original concept of transition matrices from the theory of subshifts of finite type. We prove the analyticity of the Ruelle’s operator and present some examples.     

A MIP formulation for the minmax regret total completion time in scheduling with unrelated parallel machines

The paper proposes a Mixed Integer Programming (MIP) formulation of the scheduling problem with total flow criterion on a set of parallel unrelated machines under an uncertainty context about the processing times. To model the problem we assume that lower and upper bounds are known for each processing time. In this context we consider an optimal minmax regret schedule as a suitable approximation to the optimal schedule under an arbitrary choice of the possible processing times.     

Risk models for the Prize Collecting Steiner Tree problems with interval data

Given a connected graph G=(V,E)with a nonnegative cost on each edge in E,a nonnegative prize at each vertex in V,and a target set V′V,the Prize Collecting Steiner Tree(PCST)problem is to find a tree T in G interconnecting all vertices of V′such that the total cost on edges in T minus the total prize at vertices in T is minimized.The PCST problem appears frequently in practice of operations research.While the problem is NP-hard in general,it is polynomial-time solvable when graphs G are restricted to series-parallel graphs.In this paper,we study the PCST problem with interval costs and prizes,where edge e could be included in T by paying cost xe∈[c e,c+e]while taking risk(c+e xe)/(c+e c e)of malfunction at e,and vertex v could be asked for giving a prize yv∈[p v,p+v]for its inclusion in T while taking risk(yv p v)/(p+v p v)of refusal by v.We establish two risk models for the PCST problem with interval data.Under given budget upper bound on constructing tree T,one model aims at minimizing the maximum risk over edges and vertices in T and the other aims at minimizing the sum of risks over edges and vertices in T.We propose strongly polynomial-time algorithms solving these problems on series-parallel graphs to optimality.Our study shows that the risk models proposed have advantages over the existing robust optimization model,which often yields NP-hard problems even if the original optimization problems are polynomial-time solvable.     

Approximate dynamic programming for stochastic N-stage optimization with application to optimal consumption under uncertainty

Stochastic optimization problems with an objective function that is additive over a finite number of stages are addressed. Although Dynamic Programming allows one to formally solve such problems, closed-form solutions can be derived only in particular cases. The search for suboptimal solutions via two approaches is addressed: approximation of the value functions and approximation of the optimal decision policies. The approximations take on the form of linear combinations of basis functions containing adjustable parameters to be optimized together with the coefficients of the combinations. Two kinds of basis functions are considered: Gaussians with varying centers and widths and sigmoids with varying weights and biases. The accuracies of such suboptimal solutions are investigated via estimates of the error propagation through the stages. Upper bounds are derived on the differences between the optimal value of the objective functional and its suboptimal values corresponding to the use at each stage of approximate value functions and approximate policies. Conditions under which the number of basis functions required for a desired approximation accuracy does not grow “too fast” with respect to the dimensions of the state and random vectors are provided. As an example of application, a multidimensional problem of optimal consumption under uncertainty is investigated, where consumers aim at maximizing a social utility function. Numerical simulations are provided, emphasizing computational pros and cons of the two approaches (i.e., value-function approximation and optimal-policy approximation) using the above-mentioned two kinds of basis functions. To investigate the dependencies of the performances on dimensionality, the numerical analysis is performed for various numbers of consumers. In the simulations, discretization techniques exploiting low-discrepancy sequences are used. Both theoretical and numerical results give insights into the possibility of coping with the curse of dimensionality in stochastic optimization problems whose decision strategies depend on large numbers of variables.     

Variations on selective separability in non-regular spaces

We study various variations on selective separability in non-regular topological spaces. We use the notions of θ-closure and θ-density to define selective versions of θ-separability. These properties are also related to topological games.